{"paper":{"title":"On the Properties of Kullback-Leibler Divergence Between Multivariate Gaussian Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","math.IT"],"primary_cat":"cs.IT","authors_text":"Ji Wang, Kenli Li, Wanwei Liu, Yufeng Zhang, Zhenbang Chen","submitted_at":"2021-02-10T15:21:53Z","abstract_excerpt":"Kullback-Leibler (KL) divergence is one of the most important divergence measures between probability distributions. In this paper, we prove several properties of KL divergence between multivariate Gaussian distributions. First, for any two $n$-dimensional Gaussian distributions $\\mathcal{N}_1$ and $\\mathcal{N}_2$, we give the supremum of $KL(\\mathcal{N}_1||\\mathcal{N}_2)$ when $KL(\\mathcal{N}_2||\\mathcal{N}_1)\\leq \\varepsilon\\ (\\varepsilon>0)$. For small $\\varepsilon$, we show that the supremum is $\\varepsilon + 2\\varepsilon^{1.5} + O(\\varepsilon^2)$. This quantifies the approximate symmetry "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.05485","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2102.05485/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}